한국수자원학회논문집 (Journal of Korea Water Resources Association)

  • 제42권5호
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  • Pages.365-374
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  • 2009
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  • 2799-8746(pISSN)
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  • 2799-8754(eISSN)
한국수자원학회 (Korea Water Resources Association)
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Gumbel 분포에 대한 도시위치공식의 비교

Comparison of Plotting Position Formulas for Gumbel Distribution

  • 김수영 (연세대학교 사회환경시스템공학부) ;
  • 허준행 (연세대학교 사회환경시스템공학부) ;
  • 신홍준 (연세대학교 사회환경시스템공학부) ;
  • 고연우 (연세대학교 사회환경시스템공학부)
  • Kim, Soo-Young (School of Civil and Environmental Engineering, Yonsei University) ;
  • Heo, Jun-Haeng (School of Civil and Environmental Engineering, Yonsei University) ;
  • Shin, Hong-Joon (School of Civil and Environmental Engineering, Yonsei University) ;
  • Kho, Youn-Woo (School of Civil and Environmental Engineering, Yonsei University)
  • 발행 : 2009.05.31
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초록

확률도시위치는 주로 도시적 해석을 통한 연최대홍수량 또는 연최대강우량의 초과확률의 추정치 산정에 사용되며 빈도해석을 통해 선정된 적정 확률분포형과 표본자료의 적합도를 도시적으로 파악할 수 있도록 해주기 때문에 오래 전부터 수문 및 수자원 분야에 널리 이용되어 왔다. 본 연구에서는 Gumbel 분포에 적합한 도시위치공식을 추정하고자 Gumbel 분포의 순서통계량과 확률가중모멘트를 이용하여 다양한 표본크기에 대한 도시위치공식의 기본식을 유도하였고, 최적화 기법 중 하나인 유전자 알고리즘을 이용하여 도시위치공식의 매개변수를 추정하였다. 또한 Gumbel 분포에 적합한 도시위치공식을 검토하고자 Gumbel 분포의 이론적인 축소변량과 본 연구에서 추정한 도시위치공식과 기존의 도시위치공식에 의해 계산된 축소변량 간의 평균제곱근오차와 편의를 비교하였다. 그 결과, Gringorten이 제안한 도시위치공식을 적용한 경우의 축소변량간 평균제곱근오차와 순서별 편의가 가장 작은 것으로 분석되었다.

Probability plotting positions are used for the graphical display of annual maximum rainfall or flood series and the estimation of exceedance probability of those values. In addition, plotting positions allow a visual examination of the fitness of probability distribution provided by frequency analysis for a given data. Therefore, the graphical approach using plotting position has been applied to many fields of hydrology and water resources planning. In this study, the plotting position formula for the Gumbel distribution is derived by using the order statistics and the probability weight moment of the Gumbel distribution for various sample sizes. And then, the parameters of plotting position formula for the Gumbel distribution are estimated by using genetic algorithm. The appropriate plotting position formulas for the Gumbel distribution are examined by the comparison of root mean square errors and biases between theoretical reduced Gumbel variates and those calculated from derived and existing plotting position formulas. As the results, Gringorten's plotting position formula has the smaller root mean square errors and biases than any other formulas.

키워드

참고문헌

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피인용 문헌

  1. Derivation of Plotting Position Formulas Considering the Coefficients of Skewness for the GEV Distribution vol.44, pp.2, 2011, https://doi.org/10.3741/JKWRA.2011.44.2.085
  2. Development of plotting position for the general extreme value distribution vol.475, 2012, https://doi.org/10.1016/j.jhydrol.2012.09.055
  3. Prediction of Local Scour Around Bridge Piers Using GEP Model vol.34, pp.6, 2014, https://doi.org/10.12652/Ksce.2014.34.6.1779